Overcoming chemotherapy resistance in low-grade gliomas: A computational approach

Abstract

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas.

Fig 1. Visualization of the resistance acquisition process and its translation to biological interactions between populations.

(A) At the beginning of TMZ treatment, there are only sensitive cells (blue). When TMZ is administered, some sensitive cells enter a persistent state (orange) and others are damaged (green). Under continuous administration of TMZ, cells acquire a fully resistant phenotype (red). (B) Diagram of interactions between the different populations as modeled by Eqs (1–6). Sensitive cells proliferate at a rate ρ₁. When TMZ is administered, some sensitive cells are damaged at a rate ψ and enter the persistent state at a rate α₁ under the exposure to TMZ. Persister cells can return to a sensitive state at a rate β or give raise to a fully resistant phenotype at a rate α₂ if TMZ exposure continues. Damaged cells die due to mitotic catastrophe at a rate τ, while resistant cells grow at a rate ρ₂. Assumptions are based on biological experiments and clinical observations of patients diagnosed with LGGs.

Fig 2. TMZ administration protocols.

Each arrow represents an oral administration of TMZ. The C28 protocol (C for cyclic) consists of a given number of cycles of one dose per day for 5 consecutive days, followed by 23 days of rest. The ID protocol (ID for individual dose) consists of spacing the individual doses by a given number of weeks, in this example one (ID7) or two (ID14).

Fig 3. The model describes the longitudinal evolution of the tumor volume.

Fits of all patients longitudinal growth to the model Eqs (1–6) obtained by minimizing the root mean square error between data and the model. These patients mainly received a cyclic TMZ treatment (yellow background), some of them also received radiotherapy (red background) and one of them received both (light brown). (A-F) Volumetric data were acquired by ellipsoidal approximation from the MRI images, error bars represent 18% of error on tumor volume. (G) Volumetric data were acquired by precise semi-automatic segmentation and therefore no error bars were included. Each volume associated to a cellular population of the model was represented by its own curve. Each dose induced drives sensitive cells into either the damaged or the persister cell compartments. Without a supplementary dose, persister cells go back to the sensitive phenotype. Whereas, with a supplementary dose, a small proportion of persistent cells become resistant. As the simulation progresses, resistant cells become the majority and the tumor no longer responds to TMZ.

Fig 4. Effect of different time intervals between individual doses on tumor growth.

Simulation of different experimental protocols consisting of spacing each single dose by a given number of days, from 7 to 98. This patient received 80 doses of TMZ according to the classic cyclic protocol (black line). The longer the interval between doses, the longer the time to reach fatal volume (OS). However, tumor control is lost from 42 days between each dose. Error bars represent 18% of error. Inferior horizontal line shows minimum attained volume.

Fig 5. ID protocols have a better survival curve than the classic C28 protocol.

Kaplan-Meier survival curves of four virtual clinical trials which consisted of comparing C28 protocol with the administration of individual TMZ doses spaced by: (A) 7 days (ID7), (B) 14 days (ID14), (C) 21 days (ID21), and (D) 28 days (ID28). Each arm consists of 100 virtual patients. TMZ treatment was initiated 30 days after the start of the simulation for all patients. p-values were calculated using the log-rank test.

Fig 6. Compromise between OS and tumor shrinkage.

(A) Boxplot showing the survival gain (calculated at median of Kaplan-Meier curves) of different ID protocols versus the C28 one. For each protocol, 20 clinical trials with 100 patients per arm were simulated. (B) Boxplot showing the maximum volume loss when the time between individual doses is spaced from 7 to 42 days. For each protocol 500 patients were simulated.

Fig 7. Required number of patients to prove the benefits of ID protocols.

p-value matrices of (A) ID14 protocol versus C28 protocol and (B) ID21 protocol versus C28 protocol. Each column represents an independent clinical trial in which the number of patients was progressively increased. The probability of obtaining a significant trial applying the ID14 protocol is 100% with 40 or more patients per arm. However, for the ID21 protocol, at least 30 patients per arm are needed.

Fig 8. Adaptive therapy joint with ID protocols may ameliorate the toxicity of the treatment while maintaining the survival gain.

(A) Time evolution of tumor volume for a virtual glioma patient undergoing TMZ under two different protocols. The black line corresponds to an ID21 protocol where 50 doses are equally spaced in time. The time at the end of the dose is indicated with a vertical dotted orange line. The pink line corresponds to the tumor volume with that same ID protocol but applying an adaptive variation. In this case, the patient is screened every 90 days (gray dashed lines). During the next interval between screenings, the doses are only applied if the tumor volume is higher than a certain proportion (taken as the 80% here) of the initial volume. The time periods when the doses are applied are indicated by a yellow background. (B) Results of the virtual clinical trial were generated by comparing the ID14 protocol with its adaptive variation using a threshold of 50% of the initial tumor volume. (C) Results of the virtual clinical trial were generated by comparing the ID21 protocol with its adaptive variation using a threshold of 50% of the initial tumor volume.